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ASIACRYPT
2006
Springer

The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography

11 years 3 months ago
The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suitable for cryptography. Since low class number might be seen as a potential threat, it is of interest to push the method as far as possible. We have thus designed a new algorithm for the construction of CM invariants of genus 2 curves, using 2-adic lifting of an input curve over a small finite field. This provides a numerically stable alternative to the complex analytic method in the first phase of the CM method for genus 2. As an example we compute an irreducible factor of the Igusa class polynomial system for the quartic CM field Q(i
Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe
Added 20 Aug 2010
Updated 20 Aug 2010
Type Conference
Year 2006
Where ASIACRYPT
Authors Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe Ritzenthaler, A. Weng
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